{"type":"ScholarlyArticle","title":"Mixed Strategies for Security Games with General Defending Requirements","authors":[{"name":"Rufan Bai","slug":"rufan-bai","given":"Rufan","family":"Bai","affiliation":"IoTSC , University of Macau"},{"name":"Haoxing Lin","slug":"haoxing-lin","given":"Haoxing","family":"Lin","affiliation":"National University of Singapore; University of Macau."},{"name":"Xinyu Yang","slug":"xinyu-yang","given":"Xinyu","family":"Yang","affiliation":"IoTSC , University of Macau"},{"name":"Xiaowei Wu","slug":"xiaowei-wu","given":"Xiaowei","family":"Wu","affiliation":"IoTSC , University of Macau"},{"name":"Minming Li","slug":"minming-li","given":"Minming","family":"Li","affiliation":"City University of Hong Kong"},{"name":"Weijia Jia","slug":"weijia-jia","given":"Weijia","family":"Jia","affiliation":"BNU-UIC; Beijing Normal University (Zhuhai )"}],"abstract":"The Stackelberg security game is played between a defender and an attacker, where the defender needs to allocate a limited amount of resources to multiple targets in order to minimize the loss due to adversarial attack by the attacker. While allowing targets to have different values, classic settings often assume uniform requirements to defend the targets. This enables existing results that study mixed strategies (randomized allocation algorithms) to adopt a compact representation of the mixed strategies.\r\nIn this work, we initiate the study of mixed strategies for the security games in which the targets can have different defending requirements. In contrast to the case of uniform defending requirement, for which an optimal mixed strategy can be computed efficiently, we show that computing the optimal mixed strategy is NP-hard for the general defending requirements setting. However, we show that strong upper and lower bounds for the optimal mixed strategy defending result can be derived. We propose an efficient close-to-optimal Patching algorithm that computes mixed strategies that use only few pure strategies. We also study the setting when the game is played on a network and resource sharing is enabled between neighboring targets. Our experimental results demonstrate the effectiveness of our algorithm in several large real-world datasets.","doi":"10.24963/ijcai.2022/7","url":"https://ijcai.org/proceedings/2022/7","pdf":"https://ijcai.org/proceedings/2022/0007.pdf","markdown":"https://ijcai.org/proceedings/2022/7.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/7","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":7,"pages":{"first":46,"last":52},"keywords":["Constraint Satisfaction and Optimization: Constraint Optimization","Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Resource Allocation","Multidisciplinary Topics and Applications: Smart Cities"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986712","length_sec":92,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984855","length_sec":357,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Acemoglu et al., 2016] Daron Acemoglu, Azarakhsh Malekian, and Asuman E. 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